Whisk the yolks and sugar together until pale yellow.
Warm the milk, cream, and nutmeg until it just lightly simmers.
Temper the egg/sugar mixture with the milk/cream mixture.
Return to the saucepan and cook until thickened, stirring slowly and constantly. It should get to 170°F.
Remove from heat. Stir in the rum/bourbon. Chill in the refrigerator at least 4 hours, and up to overnight.
The next day, add your chilled ice cream to your ice cream maker. Churn (stir setting) until it is the thickness of soft serve ice cream, ~20 minutes. You can enjoy it now as soft serve, or continue to final step for ice cream consistency.
Transfer to a container you can freeze, cover with parchment paper if it doesn't have a lid, and freeze at least 4 hours.
Notes
If you cannot wait the 4 hours to chill the ice cream before churning it, you can chill it quickly over a bowl filled with ice water. Just stir the ice cream to cool the base faster than your refrigerator can.
Do not add more rum/bourbon than advised in the recipe or the ice cream will not solidify.